login
A292919
Sum of n-th powers of odd divisors of n.
5
1, 1, 28, 1, 3126, 730, 823544, 1, 387440173, 9765626, 285311670612, 531442, 302875106592254, 678223072850, 437893920912786408, 1, 827240261886336764178, 150094635684419611, 1978419655660313589123980, 95367431640626, 5842587018944528395924761632, 81402749386839761113322
OFFSET
1,3
FORMULA
a(n) = [x^n] Sum_{k>=1} (2*k - 1)^n*x^(2*k-1)/(1 - x^(2*k-1)).
a(2^k) = 1.
MAPLE
f:= proc(n) local t, d;
t:= n/2^padic:-ordp(n, 2);
add(d^n, d = numtheory:-divisors(t));
end proc:
map(f, [$1..30]); # Robert Israel, Sep 27 2017
MATHEMATICA
Rest[Table[SeriesCoefficient[Sum[(2 k - 1)^n x^(2 k - 1)/(1 - x^(2 k - 1)), {k, 1, n}], {x, 0, n}], {n, 0, 22}]]
f[n_] := Plus @@ (Select[Divisors[n], OddQ]^n); Array[f, 22] (* Robert G. Wilson v, Sep 26 2017 *)
PROG
(PARI) a(n) = sumdiv(n, d, if (d%2, d^n)); \\ Michel Marcus, Sep 08 2018
CROSSREFS
Diagonal of A285425.
Sequence in context: A051000 A132057 A363590 * A040777 A036568 A040776
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Sep 26 2017
STATUS
approved